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Simplifying 0 = 3x2 + -30x + 60 Reorder the terms: 0 = 60 + -30x + 3x2 Solving 0 = 60 + -30x + 3x2 Solving for variable 'x'. Combine like terms: 0 + -60 = -60 -60 + 30x + -3x2 = 60 + -30x + 3x2 + -60 + 30x + -3x2 Reorder the terms: -60 + 30x + -3x2 = 60 + -60 + -30x + 30x + 3x2 + -3x2 Combine like terms: 60 + -60 = 0 -60 + 30x + -3x2 = 0 + -30x + 30x + 3x2 + -3x2 -60 + 30x + -3x2 = -30x + 30x + 3x2 + -3x2 Combine like terms: -30x + 30x = 0 -60 + 30x + -3x2 = 0 + 3x2 + -3x2 -60 + 30x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -60 + 30x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-20 + 10x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-20 + 10x + -1x2)' equal to zero and attempt to solve: Simplifying -20 + 10x + -1x2 = 0 Solving -20 + 10x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 20 + -10x + x2 = 0 Move the constant term to the right: Add '-20' to each side of the equation. 20 + -10x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + -10x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -10x + x2 = 0 + -20 -10x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 -10x + x2 = -20 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -20 + 25 Reorder the terms: 25 + -10x + x2 = -20 + 25 Combine like terms: -20 + 25 = 5 25 + -10x + x2 = 5 Factor a perfect square on the left side: (x + -5)(x + -5) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (x + -5) equal to 2.236067978 and -2.236067978.Subproblem 1
x + -5 = 2.236067978 Simplifying x + -5 = 2.236067978 Reorder the terms: -5 + x = 2.236067978 Solving -5 + x = 2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 2.236067978 + 5 Combine like terms: -5 + 5 = 0 0 + x = 2.236067978 + 5 x = 2.236067978 + 5 Combine like terms: 2.236067978 + 5 = 7.236067978 x = 7.236067978 Simplifying x = 7.236067978Subproblem 2
x + -5 = -2.236067978 Simplifying x + -5 = -2.236067978 Reorder the terms: -5 + x = -2.236067978 Solving -5 + x = -2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -2.236067978 + 5 Combine like terms: -5 + 5 = 0 0 + x = -2.236067978 + 5 x = -2.236067978 + 5 Combine like terms: -2.236067978 + 5 = 2.763932022 x = 2.763932022 Simplifying x = 2.763932022Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.236067978, 2.763932022}Solution
x = {7.236067978, 2.763932022}
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